A method of the kind to which the present invention relates is known from U.S. Pat. No. 4,346,514. In this known method, components are picked up by placement heads and are then placed simultaneously on the carriers. When several components are placed by a placement head on the same carrier, a placement head must perform a movement in the x,y plane. A disadvantage of the method described above is that a separate driving mechanism for each placement head is required for performing these x,y movements.